I’ve given this a little more thought, and I found a 21.5” monitor that’s only 1.2” thick with VESA mount capability. At that size, it fits within the 12” opening of the frame of my Facade.
I was gonna buy a vinyl logo to put on a fourth facade panel I already made, but I could mount the monitor in that frame instead, and display my logo on the monitor. I already have an a second video output from the light control/backup PC in my Large System that I put there for connecting to a projector, which I have not ever used for a DJ gig. It would be easy to use that port for the Facade-mounted monitor.
I think I’m gonna do it.

The only drawback on the monitor I can see is the way the power and video connectors are situated...
...cables would stick straight out (rather than down). I think there’s enough room to deal with that though. There was a complaint in the review about the size of the power supply plug... doesn’t use an IEC plug, but has an external power supply. I think I can deal with that pretty easily too.

For just $100 for the monitor and other materials (and the facade panel I already have), what the heck???